Double-butted spokes are thicker at the ends than in the middle. The most popular diameters are 2.0/1.8/2.0 mm (also known as 14/15 gauge) and 1.8/1.6/1.8 (15/16 gauge).
Double-butted spokes do more than save weight. The thick ends make them as strong in the highly-stressed areas as straight-gauge spokes of the same thickness, but the thinner middle sections make the spokes effectively more elastic, allowing them to stretch (temporarily) more than thicker spokes.
As a result, when the wheel is subjected to sharp localized stresses, the most heavily-stressed spokes can elongate enough to shift some of the stress to adjoining spokes. This is particularly desirable when the limiting factor is how much stress the rim can withstand without cracking around the spoke holes.